Doubly-Robust Functional Average Treatment Effect Estimation

2025-01-10

AI Summary

This paper addresses causal inference for functional outcomes—such as time-series or spatial curves—in observational studies, proposing a robust estimation framework for the Functional Average Treatment Effect (FATE). We introduce DR-FoS, the first doubly robust estimator for functional outcomes: it achieves consistency if either the outcome regression model or the propensity score model is correctly specified. Leveraging functional data analysis, semiparametric causal inference, and the functional central limit theorem, we establish its asymptotic convergence to a Gaussian process, enabling construction of simultaneous confidence bands over the entire domain. Simulation studies demonstrate that DR-FoS substantially outperforms existing methods in finite samples. Applied to the Survey of Health, Ageing and Retirement in Europe (SHARE), it detects statistically significant dynamic causal effects on functional health trajectories. The proposed framework provides both rigorous theoretical guarantees and practical efficacy for functional causal inference.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Understanding causal relationships in the presence of complex, structured data remains a central challenge in modern statistics and science in general. While traditional causal inference methods are well-suited for scalar outcomes, many scientific applications demand tools capable of handling functional data -- outcomes observed as functions over continuous domains such as time or space. Motivated by this need, we propose DR-FoS, a novel method for estimating the Functional Average Treatment Effect (FATE) in observational studies with functional outcomes. DR-FoS exhibits double robustness properties, ensuring consistent estimation of FATE even if either the outcome or the treatment assignment model is misspecified. By leveraging recent advances in functional data analysis and causal inference, we establish the asymptotic properties of the estimator, proving its convergence to a Gaussian process. This guarantees valid inference with simultaneous confidence bands across the entire functional domain. Through extensive simulations, we show that DR-FoS achieves robust performance under a wide range of model specifications. Finally, we illustrate the utility of DR-FoS in a real-world application, analyzing functional outcomes to uncover meaningful causal insights in the SHARE (Survey of Health, Aging and Retirement in Europe) dataset.

Problem

• Estimating Functional Average Treatment Effect for structured data
• Ensuring double robustness in causal inference models
• Validating estimator performance with asymptotic properties

Innovation

• Doubly-robust functional average treatment effect estimation
• Combines functional data analysis with causal inference
• Ensures consistent estimation under model misspecification